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Maharaja Ranjit Singh Punjab Technical University, Punjab, Mechanical Engineering Semester 1, Mathematics-I (Calculus, Linear Algebra) Syllabus

Mathematics-I (Calculus, Linear Algebra) Lecture notes | Videos | Free pdf Download | Previous years solved question papers | MCQs | Question Banks| Syllabus

Unit - 1 Calculus

1.1 Rolle’s theorem Mean value theorems

1.2 Taylor’s and Maclaurin theorems with remainders

1.3 Indeterminate forms and LHospitals rule

1.4 Maxima and minima

1.5 Evaluation of definite and improper integrals

1.6 Beta and Gamma functions and their properties

1.7 Applications of definite integrals to evaluate surface areas and volumes of revolutions

Unit - 2 Sequence and Series

2.1 Convergence of sequence and series

2.2 Comparison test

2.3 Ratio test

2.4 Raabe’s test

2.5 Logarithmic test

2.6 Cauchy’s root test

2.7 Cauchy’s Integral test

2.8 Series of positive and negative terms Power series Taylors series

2.9 Series for exponential trigonometric and logarithm functions

Unit - 3 Multivariable Calculus

3.1 Limit continuity and partial derivatives total derivative

3.2 Tangent plane and normal line

3.3 Maxima minima and saddle points

3.4 Method of Lagrange multipliers

3.5 Gradient curl and divergence Geometrical interpretation and basic properties

3.6 Directional derivative

Unit - 4 Linear Algebra

4.1 Inverse and rank of a matrix

4.2 Ranknullity theorem

4.3 System of linear equations

4.4 Symmetric skewsymmetric and orthogonal matrices

4.5 Determinants

4.6 Eigenvalues and eigenvectors

4.7 Diagonalization of matrices

4.8 CayleyHamilton Theorem and Orthogonal transformation